ipython_notebooks/dm-logo2.html at master · terryspitz/ipython_notebooks · GitHub

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%%javascript


function reuleaux(i, j, k) {
    //if(j==0) return reuleaux(i, 20, k-1) //flatten off edge
    var rad = (j / 10.0 - 1) * Math.PI / 3.0
    //using Polar equation of a curve from https://en.wikipedia.org/wiki/Polar_coordinate_system
    //R=1, r0=1/sqrt(3) (2/3 height of unit sided equilateral triangle, offset of centre of reuleaux arc)
    var cosr = Math.cos(rad)
    var r = (Math.sqrt(4.0/3.0*cosr*cosr + 8.0/3.0) - 2.0/Math.sqrt(3.0)*cosr)/2.0
    var az = i / 50.0 * Math.PI * 2.0
    var rot = az*2/3
    if(0<=rot && rot<Math.PI/6){
        var r0 = 1-Math.cos(rot)/Math.sqrt(3.0)
    }else if(1*Math.PI/6<=rot && rot<3*Math.PI/6){
        var r0 = Math.cos(rot-2*Math.PI/6)/Math.sqrt(3.0)
    }else if(3*Math.PI/6<=rot && rot<5*Math.PI/6){
        var r0 = 1-Math.cos(rot-4*Math.PI/6)/Math.sqrt(3.0)
    }else if(5*Math.PI/6<=rot && rot<7*Math.PI/6){
        var r0 = Math.cos(rot-6*Math.PI/6)/Math.sqrt(3.0)
    }else if(7*Math.PI/6<=rot && rot<9*Math.PI/6){
        var r0 = 1-Math.cos(rot-8*Math.PI/6)/Math.sqrt(3.0)
    }else if(9*Math.PI/6<=rot && rot<11*Math.PI/6){
        var r0 = Math.cos(rot-10*Math.PI/6)/Math.sqrt(3.0)
    }else if(11*Math.PI/6<=rot && rot<=12*Math.PI/6){
        var r0 = 1-Math.cos(rot-12*Math.PI/6)/Math.sqrt(3.0)
    }
    var th = rad + k*Math.PI*2/3 + rot //twist it!

    //based on parametric equation of a torus
    var x = Math.sin(-az)* (r * Math.cos(th) - r0 - 0.5)
    var y = Math.cos(-az)* (r * Math.cos(th) - r0 - 0.5)
    var z = r*Math.sin(th)
    return {x: x, y: z, z: y}
}

with_mathbox(element, function(mathbox) {
    var view = mathbox.cartesian({scale: [0.5, 0.5, 0.5]})
    .unit({scale:1000})
    view.voxel({
        width: 50, height: 20, depth: 3,
        items: 4, channels: 3,
        expr: function (emit, i, j, k, t) {
            var p0 = reuleaux(i,j,k); emit(p0.x, p0.y, p0.z)
            var p1 = reuleaux(i+1,j,k); emit(p1.x, p1.y, p1.z);
            var p2 = reuleaux(i+1,j+1,k); emit(p2.x, p2.y, p2.z);
            var p3 = reuleaux(i,j+1,k); emit(p3.x, p3.y, p3.z);
        }
    })
    for(var i=0; i<=0; ++i)
    for(var j=0; j<=0; ++j)
        view.transform({position: [-j*3.5, 0, -i*3.5]})
            .transform({rotation: [(0, 0, 0)]})
            .face({color: (i==0 && j==0 )?0x60B0FF : 0xEEEEEE, shaded: false})
            .face({color: (i==0 && j==0 )?0x60B0FF : 0xEEEEEE, shaded: true, opacity: 0.5})
})